Fixed Point Theorems On Cone B-Metric Space

In this paper, the existence and uniqueness of the fixed points for some kinds of contractive mapping are obtained in the cone b-mctric space by the method of iterative sequence, such that Edelstein contractive mapping, Suzuki contractive mapping, four weakly compatible self-mapping. The results are as follows:1. We mainly study the existence and uniqueness of the fixed points for Edelstein contractive mapping without the assumption of normality, and give the fixed point theorems for two different types of contractive mapping. An example is given to demonstrate the importance of the results.2. We present the existence and uniqueness of the fixed points for two differ-ent types of Suzuki contractive mapping without the assumption of normality.3. By using the weakly compatibility of self-mapping on cone b-metric space, we discuss the existence and uniqueness of common fixed points for four self-mapping by increasing the contractive conditions, and obtain a new common fixed point theorem.